Indicating Possession Between You and Another Person
"The party's at Bob's and my house."
Despite however "clunky" you think this sounds, this way is correct. There's nothing ungrammatical with this.
See the following references:
https://www.english-grammar-revolution.com/possessive-pronoun.html (scroll down to "Compound Possessive Nouns and Pronouns")
https://ontariotraining.net/grammar-tip-possession-with-compound-nouns-and-pronouns/
https://erinwrightwriting.com/compound-possessive-pronoun-strings-or-who-owns-that-dog-anyway/